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arXiv:1401.3773 · Journal of Physics Conference Series

Collapse models and perceptual processes

G. C. Ghirardi, Raffaele Romano

Published Apr 14, 2014• 2 citations

Abstract

Theories including a collapse mechanism have been presented various years ago. They are based on a modification of standard quantum mechanics in which nonlinear and stochastic terms are added to the evolution equation. Their principal merits derive from the fact that they are mathematically precise schemes accounting, on the basis of a unique universal dynamical principle, both for the quantum behavior of microscopic systems as well as for the reduction associated to measurement processes and for the classical behavior of macroscopic objects. Since such theories qualify themselves not as new interpretations but as modifications of the standard theory they can be, in principle, tested against quantum mechanics. Recently, various investigations identifying possible crucial test have been discussed. In spite of the extreme difficulty to perform such tests it seems that recent technological developments allow at least to put precise limits on the parameters characterizing the modifications of the evolution equation. Here we will simply mention some of the recent investigations in this direction, while we will mainly concentrate our attention to the way in which collapse theories account for definite perceptual process. The differences between the case of reductions induced by perceptions and those related to measurement procedures by means of standard macroscopic devices will be discussed. On this basis, we suggest a precise experimental test of collapse theories involving conscious observers. We make plausible, by discussing in detail a toy model, that the modified dynamics can give rise to quite small but systematic errors in the visual perceptual process.

DOI: 10.1088/1742-6596/504/1/012022

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Theories including a collapse mechanism have been presented various years ago. They are based on a modification of standard quantum mechanics in which nonlinear and stochastic terms are added to the evolution equation. Their principal merits derive from the fact that they are mathematically precise schemes accounting, on the basis of a unique universal dynamical principle, both for the quantum behavior of microscopic systems as well as for the reduction associated to measurement processes and for the classical behavior of macroscopic objects. Since such theories qualify themselves not as new interpretations but as modifications of the standard theory they can be, in principle, tested against quantum mechanics. Recently, various investigations identifying possible crucial test have been discussed. In spite of the extreme difficulty to perform such tests it seems that recent technological developments allow at least to put precise limits on the parameters characterizing the modifications of the evolution equation. Here we will simply mention some of the recent investigations in this direction, while we will mainly concentrate our attention to the way in which collapse theories account for definite perceptual process. The differences between the case of reductions induced by perceptions and those related to measurement procedures by means of standard macroscopic devices will be discussed. On this basis, we suggest a precise experimental test of collapse theories involving conscious observers. We make plausible, by discussing in detail a toy model, that the modified dynamics can give rise to quite small but systematic errors in the visual perceptual process.

Spontaneous collapse models have been proposed as a possible realist solution of the quantum measurement problem. They assume that the standard unitary evolution is valid only in the microscopic limit, with stochastic corrections leading to a dynamical reduction of the wave function at macroscopic level. A remarkable feature of collapse models is that, unlike interpretations of quantum mechanics, they predict departures from standard theory that can be experimentally tested. A common prediction is a violation of energy conservation, which manifests as an universal force noise acting on mechanical systems. Here, we will discuss recent bounds on collapse models set by mechanical experiments, focusing on ultracold cantilevers and gravitational wave detectors. First notable results are a partial exclusion of the CSL parameters proposed by Adler and a full exclusion of an early model based on quantum gravity arguments.

Abstract The collapse of the wavefunction is arguably the least understood process in quantum mechanics. A plethora of ideas---macro-micro divide, many worlds and even consciousness---have been put forth to resolve the issue. Contrary to the standard Copenhagen interpretation, objective collapse models modify the Schrödinger equation with nonlinear and stochastic terms in order to explain the collapse of the wavefunction. In this paper we propose a collapse model in which a particle's wavefunction has a possibility of collapsing when it interacts with macroscopic objects, without the intervention of a conscious observer. We propose four possible conditions of collapse of the wavefunction and make testable predictions which differ from standard quantum mechanics.

Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic process, and most theories violate energy conservation. In this paper we hypothesise that the collapse of wavefunctions can be caused by interactions with other objects (macroscopic or microscopic) and energy is conserved in that process. To test various hypotheses regarding collapse of wavefunctions, we propose a model system which is the quantum analogue of a classical soft-impact oscillator. We propose some alternative postulates regarding the conditions for and the result of a collapse, and obtain the implication of each on the behavior of observable quantities, which can possibly be experimentally tested.

The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schrödinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems—therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space. We will review these basic features. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. Although they are difficult to detect, we discuss the most relevant scenarios, where such deviations can be observed.

Quantum mechanics is an extremely successful theory that agrees with every experimental test. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse: a stochastic nonlinear modification of the Schr\"odinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: trace dynamics and gravity-induced collapse. As the macroscopic scale is approached, predictions of this proposal begin to differ appreciably from those of quantum theory and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. It is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.

The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schroedinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. We also discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics.